Gravity dam



Patented Apr. 28, 1936 UNITED STATES PATENT OFFICE GRAVITY DAM Louis Urbain Edgar Antonin Baticle, Paris, France 2 Claims.

It is known that the standard gravity dam is of substantially triangular section, the angle inclination of the upstream side being approximately zero and the angle of inclination of the 5' downstream side being determined in such manner that by taking account of a certain value of the underpressure there may be no expansion forces. With the same hypothesis regarding the under pressure and the same density there is obtained a constant inclination of the downstream side. It follows that the resistance to crushing of the concrete is badly utilized in dams of medium strength.

On the other hand, and in order to avoid the effects of infiltration in the large masses of concrete of which these dams are formed, drain ducts have been provided which produce certain strains and to a certain extent reduce the homogeneity on which resistance calculations are based.

In order to avoid these disadvantages it has been proposed to use hollow dams constituted by true arches transferring the pressures to which they are subjected to gravity pillars resisting forces tending to overturn the dam. Dams thus 5 formed are more economical of material, but they possess the serious disadvantage of great uncertainty in the working conditions of the arched portions, the most improved methods of calculation being based on hypotheses more or less subject to caution. In particular, the risk is run of allowing to subsist expansion forces tending to produce horizontal cracks in the arches. Moreover the resistance to overturning is localized solely in the pillars.

The present invention permits of avoiding all these disadvantages and of obtaining the advantages of dams having multiple arches. It has for its object a dam characterized by a downstream face having a ruled surface generated by a straight line bearing at one end on the horizontal upper edge constituting the crest of the dam, remaining normal to this edge, and bearing at the other end on a directrix located in a horizontal plane, the upstream face being formed in known manner. Such a surface is called conoidal.

A solid thus delineated presents the following advantages. The mean strain on the faces of a small elementary prism cut away in the solid hav- 5 ing a section dx dy and'a length 2a may be calculated by the theory of elasticity. The mean strain on the generatrixes of the rear face is a function of the ratio of the width of the front face to that of the rear face. This ratio can be so 55 selected that this strain is equal to permissible limits, whereby maximum material economy may be obtained.

According to a preferred form of the invention the dam is constituted by adjoining elements, such that their front faces form together a con- 5 tinuous plane surface, or a polygonal surface slightly convex towards the retaining side, the rear face of each being a ruled surface having a symmetrical directrix.

The drawing represents diagrammatically an 10 embodiment of the invention. 7 In this drawing:

Fig. 1 shows the geometrical construction of an element of the dam.

Fig. 2 shows the dam as seen in plan, the usual hydraulic accessories being omitted. 15

The upper edge of the dam is indicated by the line ze. It is substantially at the maximum retaining level. The front face is the plane passing through the line 2-2.

Considering any horizontal plane whatever 20 intersecting the front face on the line 'wu, each of the elementary blocks forming the dam is bounded at the front by the faces a b a 12 extended to the foundations of the dam. The lateral faces are designated by b a; A and b a. A. 2 The rear conoidal surface is generated by the straight line mM which is displaced while remaining normal to z-z, along the generating curve A M B B A symmetrical in relation to the plane a: o :11 normal to 2 z. 3

Designating by m and 11.2 the normal molecular forces per unit of length on the lines or and oz; of a prism of section 11 a: d y and of length 22:, forces directed respectively along the axes 0a: and 0y, by t the corresponding tangential force 3 and by D the specific weight of the structure, the following equations will then obtain:-

being the equation of the ruled surface.

Assuming that and accounting for x=0, nz=a y and t=o, and for U=7Jo (on the free surface B B p p) there is obtained 7Ll"l7ot=0 and t-D'on2=0, then the wards the retaining side.

force an on the extreme surface, that is in the plane $=voy, has for value:

this force being independent of f (v), on the particular form of the directing curve. Moreover on the front face:--(upstream)- struction, that it should be as simple as possible:

a straight line or a parabola for example.

Each of the elementary blocks forming the dam balances by its weight the pressures and also any under pressures to which it is subjected,

without the help of the arch effect produced in each of the horizontal sections.

These elementary blocks are juxtaposed and united in the neighbourhood of the upstream face by horizontal reinforcements disposed in the thinner portions, to avoid undue tensions produced therein due to changes of temperature, ac-

count moreover being taken of the arch effect due to curvature of the neutral axes of the horizontal sections. They are assembled in such manner that their upstream faces form as a whole a plane or polygonal surface slightly convex to- The consideration of the elementary blocks has simply for its object to define the geometrical construction of the dam.

In practice the whole of the blocks are poured ;in horizontal layers into appropriate forms.

Fig. 2 shows diagrammatically a dam thus :constituted and comprising four'elements. The

45 dam in four equidistant planes.

dotted lines indicate horizontal sections of this The arrangements forming the subject ofthe invention present numerous advantages.

Each element balancing by its weight the pressures to which it is subjected, the arch' effect produced in each of the horizontal sections gives an increase in safety. The portions recessed due to the directing curves of the conoidal surfaces, produce a drainage much better than that obtained with the shafts and ducts of the standard massive dam. The free surface of the downstream face having a ruled surface the construction of the forms presents no difficulty,.the directing curve being defined in any horizontal plane whatever.

Considered in relation to dams having arches the dam described has the advantage that it can be calculated and will work more rationally. In relation to standard gravity dams it has the advantage of great economy of material. In fact, if for example, the two types of dams having a vertical front face are subjected to the condition wherein the compression force should be a certain fraction 7c of the hydrostatic pressure, the recessed dam subject of the present invention is bounded by the same planes as the standard gravity dams, and there is obtained fromwhich an exact measure of the economy resulting from the invention is had, the ratio of the volume of the recessed dam and of the solid standard dam being ahv and S being the area of the directing curve.

Having now particularly described and ascertained the nature of my said invention and in what manner the same is to be performed, I declare that what I claim is:

l. A gravity dam of the character described having its downstream side inclined upstream from the base and presenting a plurality of spaced, concave, conoidal surfaces from the base to the crest, the entire downstream side being defined by geometrical surfaces generated by an inclined straight line perpendicular to the crest of the dam and moved at its upper end along the crest while its lower end is simultaneously moved in symmetrically arranged curved paths at the base.

2. A gravity dam of the character described having its downstream side inclined upstream from the base and presenting spaced, concave, conoidal faces separated by plain buttress portions, the entire surface being defined by a generatrix moved at one end along the crest of the dam and at the other along alternate symmetrically disposed curves and straight paths at the base, said generatrix being always perpendicular to the crest.

LOUIS URBAIN EDGAR ANTONIN BATICLE. 

